Gamp was the surname of a pure-blood wizarding family. They were related to the Black family, and more distantly to the Macmillan and Prewett families. It is unknown if this family is still extant or pure-blood.
The only known member of this family was Hesper Black née Gamp, who married Sirius Black II, the heir of the prejudiced Black family. She was the great-grandmother of Sirius and Regulus Black. Another possible family member is the witch or wizard who discovered Gamp's Law of Elemental Transfiguration.
Behind the scenes
The Gamps were not part of the Sacred Twenty-Eight, indicating that, by the 1930s, they were either extinct in the male line or no longer pure-blood.